failure analysis of cerebral aneurysm mohd yusrizal...
TRANSCRIPT
FAILURE ANALYSIS OF CEREBRAL ANEURYSM
MOHD YUSRIZAL BIN MOHD YUSOOF
Thesis submitted in fulfillment of the requirements for the award of the degree of
Bachelor of Mechanical Engineering
Faculty of Mechanical EngineeringUNIVERSITI MALAYSIA PAHANG
DISEMBER 2010
ii
UNIVERSITI MALAYSIA PAHANG
FACULTY OF MECHANICAL ENGINEERING
I certify that the project entitled “Failure Analysis of Cerebral Aneurysm” is written
Mohd Yusrizal B. Mohd Yusoof. I have examined the final copy of this project and in
our opinion; it is fully adequate in terms of scope and quality for the award of the degree
of Bachelor of Engineering. I herewith recommend that it be accepted in partial
fulfillment of the requirements for the degree of Bachelor of Mechanical Engineering.
(Mohd Fadzil bin Abdul Rahim) ....................................
Examiner Signature
iii
SUPERVISOR’S DECLARATION
I hereby declare that I have checked this project and in my opinion, this project is
adequate in terms of scope and quality for the award of the degree of Bachelor of
Mechanical Engineering
Signature :
Name of Supervisor : Mohd Akramin Bin Mohd Romlay
Position : Lecturer
Date :
iv
STUDENT’S DECLARATION
I hereby declare that the work in this project is my own except for quotations and
summaries which have been duly acknowledged. The project has not been accepted for
any degree and is not concurrently submitted for award of other degree.
Signature :
Name : Mohd Yusrizal Bin Mohd Yusoof
ID Number : MA08148
Date :
vi
ACKNOWLEDGEMENTS
I would like to thank all people who have helped and inspired me during completed this studies.
I especially want to thank my supervisor; Mr. Mohd Akramin Bin Mohd Romlay, for his guidance during completed this project. His perpetual energy and enthusiasm in supervising had motivated his entire student, including me. In addition, he was always accessible and willing to help his students with their project. As a result, this project can be completed.
My deepest gratitude goes to my family for their unflagging love and support throughout our life; this dissertation is simply impossible without them and also to my love Siti Hana Bte Mohamad Yusoff.
All of my friends at the University Malaysia Pahang made it a convenient place to study. In particular, I would like to thank all friend for their knowledge and help in order to complete this studies.
Last but not least, thanks to God for giving us living in this universe and provide us with all necessary things.
vii
ABSTRACT
The aneurysm is the abnormal bulging of a portion of an artery due weakness in the cerebral at the circle of Willis brain. Nowadays, cerebral aneurysm is the one of the disease which have killed the people very quickly. This occurs when the mechanical behavior exceeds the strength of the tissue. This study is focused on cerebral aneurysm. Investigations on the changes of flow phenomena and the mechanical behavior in cerebral aneurysm have been studied. By using the simulation tools, the stress behavior on this region has been analyzed. The normal size of cerebral diameter is about 3-7 mm and aneurysm can bulge and reach until 10 mm. The velocity profile, nodal pressure distribution, displacement of wall and the stress at the wall had been identified at locations of aneurysm. As the size of an aneurysm increases, there was a potential of rupture of aneurysm. This can result in severe hemorrhage or even worst, fatal event.The studies are proceed based on numerical approach. The result shown that mechanical behaviors inside aneurysm region would be different compare to the normal blood vessel. It was proved that the maximum velocity had been obtained is 0.192 m/s. The maximum displacement of wall aneurysm at the neck is 0.00005 mm and the maximum affective stress at the aneurysm is 21.70 MPa. For the pressure distribution, the highestpressure at the aneurysm is 15.6 KPa. This study would help to predict cerebral aneurysm and provide better understanding about the cerebral aneurysm.
viii
ABSTRAK
Aneurisme merupakan satu salur darah dibahagian kepala yang mengalami keadaan bengkak. Gejala ini memberi kesan yang buruk kepada pesakit yang boleh menyebabkan salur darah tersebut menjadi lemah. Pada masa kini penyakit ini telah menyerang dan membunuh manusia dengan begitu cepat. Perkara ini terjadi apabila keadaan mekanikal telah melebihi keadaan asal pada salur darah tersebut. Ini kerana para doktor masih tidak dapat menyelesaikan masalah ini. Simulasi akan dijalankan dengan mengambil model salur darah ditengah otak. Kajian ini telah menfokuskan kepada keadaan mekanikal pada salur darah. Saiz normal salur darah di bahagian tengah otak adalah 3-7 mm dan pembengkakkan boleh berlaku sehingga 10 mm. Apabila saiz aneurisme meningkat, terdapat potensi untuk aneurisme pecah. Ini boleh menyebabkan pendarahan atau lebih teruk, iaitu kematian. Kajian ini hanya dijalankan dengan pendekatan pengiraan matematik tanpa melibatkan sebarang eksperimen. Berdasarkan kajian telah ditunjukkan bahawa sifat-sifat mekanikal di dalam bahagian aneurismeadalah berbeza dengan salur darah yang normal. Jelaslah terbukti bahawa halaju pada aneurisme adalah 0.192 m/s. Anjakan paling tinggi adalah 0.00005 mm dan tekanan paling tinggi adalah 21.70MPa. Tekanan berkesan paling tinggi adalah 15.6 KPa. Dengan mengkaji sifat-sifat mekanikal di bahagian salur darah aneurism yang sebenar dapat memberikan maklumat-maklumat yang berguna mereka untuk lebih memahami keadaan aneurisme yang sebenar.
ix
TABLE OF CONTENTS
PAGE
EXAMINER ii
SUPERVISOR’S DECLARATION iii
STUDENTS’S DECLARATION iv
ACKNOWLEDGEMENT v
ABSTRACT vii
ABSTRAK viii
TABLE OF CONTENTS xi
LIST OF TABLES xii
LIST OF FIGURES xiii
LIST OF ABBREVIATIONS xv
CHAPTER 1 INTRODUCTION
1.1 Cerebral Aneurysms 1
1.2 Aneurysm 3
1.2.1 Symptoms of Cerebral Aneurysm 51.2.2 Risks of Aneurysm 5
1.3 Problems Statement 6
1.4 Objectives 7
1.5 Scopes 7
CHAPTER 2 LITERATURE REVIEW
2.1 Cerebral Aneurysms 8
2.2 Finite Element Analysis (FEA) 10
2.2.1 Geometry 112.2.2 Material Model 122.2.3 Boundary Condition 15
2.3 Computation Fluid Dynamics (CFD) 16
2.3.1 Blood Flow 16
x
2.3.2 Mathematical and Numerical. 17
2.4 Fluid-Structure Interaction (FSI) 20
2.5 Summary 20
CHAPTER 3 METHODOLOGY
3.1 Introduction 20
3.2 Project Planning 20
3.3 Model Design 21
3.4 Model Analysis 22
3.4.1 Finite Element Analysis Of Cerebral Aneurysm 223.4.2 Formulation Of Cerebral Aneurysm. 243.4.3 Material Model 253.4.4 Simulations Assumption, Parameter And Boundary Conditions
253.4.5 Boundary Condition 26
3.5 Computation Fluid Dynamics (CFD) 27
3.5.1 Blood Flow 28
3.6 Fluid-Structure Interaction (FSI) 28
3.7 Software Application 29
3.8 Summary 29
CHAPTER 4 RESULTS AND DISCUSSION
4.1 Introduction 31
4.2 Mechanical Behavior in Cerebral Aneurysm 31
4.3 Displacement wall of Cerebral Aneurysm 32
4.4 Stress Distribution at the Cerebral Aneurysm 34
4.5 Pressure Distribution at Neck of Aneurysm 37
4.6 Interaction between Flow and Wall Deformation 38
4.7 Summary 40
CHAPTER 5 CONCLUSION
5.1 Conclusion 41
xi
5.2 Limitations 41
5.3 Recommendations 42
REFERENCES 43
APPENDIX A1 50
APPENDIX A2 53
APPENDIX B 71
xii
LIST OF TABLES
Table No. Title Page
3.1 Parameter of cerebral aneurysm 24
3.2 Parameter of cerebral aneurysm 26
4.1 Simulation result using Adina software with diameter 65mm 29
4.2 Result simulation 31
xiii
LIST OF FIGURES
Figure No. Title Page
1.1 Circle of Willis 2
1.2 Circle of Willis 3
1.3 Type of aneurysm 5
2.1 The geometry of simplified aneurysm containing the two part 12
2.2 Artificial model 12
2.3 The cerebral arterial system in the bottom view of brain and
schematic representation of the main arteries
13
2.4 The anatomy of healthy artery wall 14
3.1 Flow chart shown the overall flow of the process of this
project
21
3.2 Geometry of dilated vessel 24
3.3 Graph velocity versus length 26
4.1 The flow phenomena in cerebral aneurysm 29
4.2 Displacement of cerebral aneurysm 30
4.3 Graph Displacement and velocity versus diameter of cerebral
aneurysm
31
4.4 Wall displacement distribution 32
4.5 Stress distribution at the cerebral aneurysm 33
4.6 Effective stress 33
4.7 Graph displacement and stress versus velocity of cerebral
aneurysm
34
4.8 Graph displacement and effective stress versus velocity of
cerebral aneurysm
34
4.9 Graph nodal pressure versus velocity of flow 35
4.10 Red circle shown that the nodal pressure at the neck of
aneurysm at blue circle.
36
4.11 Graph velocity of flow versus displacement of cerebral
aneurysm.
37
4.12 Velocity profile in cerebral aneurysm 37
xiv
4.13 Enlargement of velocity profile in cerebral aneurysm 38
6.1 Manual user SolidWork2009 45
6.2 Diameter of circle 45
6.3 Extrude the circle 46
6.4 Dome at the middle cylinder 46
6.5 Save fail type 47
7.1 Invoke the AUI Adina 48
7.2 Analysis assumption of kinematics 49
7.3 Import parasolid file 50
7.4 Select the parasolid file 50
7.5 Structure of model 51
7.6 Apply fixity column 51
7.7 Defining the material for the solid model 52
7.8 Define element group 53
7.9 Meshing of the body 54
7.10 Create the Adina input file 54
7.11 Adina CFD 55
7.12 Number of iteration 56
7.13 Automatic Time-Stepping for Transient Analysis 57
7.14 Time step of the simulation 58
7.15 Time function of the simulation 58
7.16 Time function data for pressure specified conditions 59
7.17 Time function data for velocity specified conditions 59
7.18 Import parasolid file for fluid model 60
7.19 Applying the normal traction for the fluid model 61
7.20 Applying the velocity for the fluid model 62
7.21 Define material properties for the fluid model 63
7.22 Define element group 64
7.23 Final result of the analysis 65
xv
LIST OF ABBREVIATIONS
CA Cerebral Aneurysm
CFD Computational Fluid Dynamics
FEA Finite Element Analysis
FSI Fluid Structure Iteraction
CHAPTER 1
INTRODUCTION
1.1 CEREBRAL ANEURYSM
Cerebral aneurysms are localized dilatations of the intracranial arterial wall that
usually occur on or near the circle of Willis as shown in Figure 1.1. Rupture of intra-
cranial aneurysms is the leading cause of subarachnoid hemorrhage and often causes
significant mortality and morbidity. Solid biomechanical analysis of patient-specific
cerebral aneurysms and estimations of wall stress distribution can provide useful in-
sights into the disease process and help quantify geometric features within a physics-
based framework. Investigations on solid biomechanics of intracranial aneurysms (ICA)
have been scarce unlike for abdominal aortic aneurysms (Wang et al., 2009). The bio-
mechanics of aneurysm has been studied with great interest since aneurysm rupture is a
mechanical failure of the degenerated aortic wall and is a significant cause of death in
developed countries (David et al., 2006). Rupture of cerebrovascular lesions does not
occur very frequently, but when the disease has severe consequences for the individual.
Thus, there is an urgent need to understand the etiology of these lesions and to establish
reliable criteria by which surgeons can predict the risk of rupture and thus the need for
operation (Austin et al., 1993). Besides that, the infection can lead the body to wide ill-
ness. The greatest danger of an aneurysm is rupture, which is often a fatal event.
Cerebral aneurysms are frequently observed in the outer wall of curved vessels.
They are found in the internal carotid artery, near the apex of bifurcated vessels includ-
ing the anterior communicating artery (ACA), anterior cerebral artery and the middle
cerebral artery (MCA). Cerebral aneurysms disease has been reported to affect around
one to five percent of the population.
Although many cases of this disease are unruptured, the catastrophic consequences of
subarachnoid hemorrhage (SAH) following rupture of cerebral aneurysms make optimal
treatment of patients. Rupture of a cerebral aneurysm can be dangerous for a patient and
occurs most commonly between 40 and 60 years of age. When an aneurysm ruptures,
blood leaks from the ruptured wall into the subarachnoid space, or the brain itself, p
tentially causing serious damage. Aneurysm growth and rupt
factors; geometrical factors such as aneurysm size and shape or the ratio of the ane
rysm dome height to the neck width,
of structural proteins of the extracellular matrix in the intracranial arterial wall; and h
modynamic factors, especially wall shear stresses
Aneurysms come in a variety of shapes and siz
berry aneurysm as shown in
Figure 1.1: Circle of Willis
Source: Paal et al., 2007
Although many cases of this disease are unruptured, the catastrophic consequences of
hemorrhage (SAH) following rupture of cerebral aneurysms make optimal
treatment of patients. Rupture of a cerebral aneurysm can be dangerous for a patient and
occurs most commonly between 40 and 60 years of age. When an aneurysm ruptures,
the ruptured wall into the subarachnoid space, or the brain itself, p
tentially causing serious damage. Aneurysm growth and rupture depends on multiple
geometrical factors such as aneurysm size and shape or the ratio of the ane
the neck width, biological factors such as decreased concentration
of structural proteins of the extracellular matrix in the intracranial arterial wall; and h
modynamic factors, especially wall shear stresses
Aneurysms come in a variety of shapes and sizes. The most common ty
berry aneurysm as shown in Figure 1.2 and Figure 1.3. It is round like
2
Although many cases of this disease are unruptured, the catastrophic consequences of
hemorrhage (SAH) following rupture of cerebral aneurysms make optimal
treatment of patients. Rupture of a cerebral aneurysm can be dangerous for a patient and
occurs most commonly between 40 and 60 years of age. When an aneurysm ruptures,
the ruptured wall into the subarachnoid space, or the brain itself, po-
ure depends on multiple
geometrical factors such as aneurysm size and shape or the ratio of the aneu-
biological factors such as decreased concentration
of structural proteins of the extracellular matrix in the intracranial arterial wall; and he-
es. The most common type is a
. It is round likes a berry and con-
3
nected to the artery by a stem or neck. There are two general types of aneurysms, fusi-
form and saccular. A fusiform aneurysm is spindle-shaped without a neck. The saccular
aneurysms are the most frequent cerebral aneurysms showing a berry like outpouching
of the vessel wall: they often develop at the curved side of the vessels or at the apex of
bifurcations. A giant aneurysm is like a berry aneurysm, but it is large about one and
half inches or three centimeters or more in diameter.
Figure 1.2: Circle of Willis
Source: Paal et al., 2007
1.2 ANEURYSMS
Aneurysms are blood-filled dilation (balloon-like bulge) of a blood vessel caused
by disease or weakening of the vessel wall. Aneurysms most occur in arteries at the
base of the brain (the circle of Willis) and in the aorta (the main artery coming out of
the heart, a so-called aortic aneurysm). A sign of an arterial aneurysm is a pulsating
4
swelling that produces a blowing murmur on auscultation (the act of listening for
sounds in the body) with a stethoscope.
There are four main locations where aneurysms always happen that are Cerebral
Aneurysms or Brain, Aorta Aneurysms, Abdominal Aneurysms and Thoracic Aortic
Aneurysms. As the size of an aneurysm increases, there is an increased risk of rupture,
which can result in severe hemorrhage or other complications including sudden death.
Severe bleeding can occur if the aneurysms break or rupture. Not all aneurysms are life-
threatening. But if the bulging stretches the artery too far, this vessel may burst, causing
a person to bleed to death. An aneurysm that bleeds into the brain can lead to stroke or
death. Aneurysms usually appear in either fusiform or saccular as shown in Figure 1.3.
A fusiform aneurysms is spindle shaped without a neck. While, the second type of
aneurysms is saccular. The saccular aneurysms are the most frequent cerebral aneu-
rysms showing a berry like outpouchings of the vessel wall: they often develop at the
curved side of the vessels or at the apex of bifurcations.
Saccular
Fusiform
Figure 1.3: Types of Aneurysms
Source: Paal et al., 2007
5
1.2.1 Symptoms of Cerebral Aneurysm
Symptoms will depend upon the location of the aneurysm. Common sites that
aneurysms occurred include the abdominal aortic artery, the intracranial muscles (sup-
plying blood to the brain), and the aorta (supplying blood to the chest area). Many aneu-
rysms are present without symptoms and are discovered by feeling or on x-ray films
during a routine examination. When symptoms occur, they include a pulsing sensation,
and there may be pain if the aneurysm is pressing on internal organs. If the aneurysm is
in the chest area, for example, there may be pain in the upper back, difficulty in swal-
lowing, coughing or hoarseness. A ruptured aneurysm usually produces sudden and se-
vere pain, and depending on the location and amount of bleeding, shock, loss of con-
sciousness and death. Emergency surgery is necessary to stop the bleeding.
In some cases, the aneurysm may leak blood, causing pain without the rapid de-
terioration characteristic of a rupture. Also, clots often form in the aneurysm, creating
danger of embolisms in distant organs. In some cases, the aneurysm may dissect into the
wall of an artery, blocking some of the branches. Dissecting aneurysms usually occur in
the aortic arch (near its origin, as it leaves the heart) or start in the descending thoracic
portion of the aorta after it gives off the branches to the head and arms. Symptoms vary
according to the part of the body that is being deprived of blood; they are usually sud-
den, severe and require emergency treatment.
1.2.2 Risks of Aneurysm
It is not clear exactly what causes aneurysms. However some theories and risk fac-
tors had been defined. The condition that causes the walls of the arteries to weaken can
lead to an aneurysm.
i. Genetic factor.
ii. Smoking
iii. High blood pressure
iv. High cholesterol
v. Gender factor. Male gender is likely to have aneurysm than female.
6
vi. Obesity
Aneurysms develop slowly over many years and often have no symptoms. Some-
times people do not realize they have an aneurysm that can lead to rupture. The symp-
toms of rupture include:
i. Abdominal mass
ii. Abdominal rigidity
iii. Headache
iv. Anxiety
v. Clammy skin
vi. Nausea and vomiting
vii. Pain in the abdomen or back, severe, sudden, persistent, or constant.
viii. Ringing in the ears
ix. Pulsating sensation in the abdomen
x. Rapid heart rate when rising to a standing position
xi. Shock
1.3 PROBLEMS STATEMENT
Nowadays, the case of rupture of celebrals is increasing every years and it often oc-
curs without any preceding symptoms. The rupture occurs when the stress acting artery
on the brain exceeds the strength of the artery wall itself. It was necessary to establish
reliable criteria of the rupture risk assessment procedures in cerebral for these lesions,
and criteria based on the mechanical field. Besides that, the prediction of rupture hap-
pens is not available yet. The stress distribution caused by pressure in the artery is one
element factor that influenced the rupture of aneurysm. So it was necessary to study the
behavior of these elements to better understanding of aneurysms.
7
1.4 OBJECTIVE
The objectives of this research are;
To determine maximum displacement at the wall cerebral aneurysm.
To determine stress distribution in cerebral aneurysm.
To determine the maximum pressure in the cerebral aneurysms.
1.5 PROJECT SCOPE
This project is to investigate the condition of wall ruptured in cerebral with
ADINA software. A model of cerebral with shape was created with geometry in 3D.
The flow and structure of model of cerebral aneurysm are analyzed by using Fluid-
Structure Interaction of ADINA software. The flow in cerebral, only the aneurysm from
artery brain area were selected. For this case, the project is focused on steady state of
analysis of fluid structure iteration.
CHAPTER 2
LITERATURE REVIEW
2.1 CEREBRAL ANEURYSMS
Arterial aneurysms are localized dilatations of blood vessels caused by a
congenital or acquired weakness of the media. A variety of characteristic geometries
can be distinguished. In the cerebral arteries the most common type is the saccular
aneurysm, having a bubble-like geometry. Most cerebral aneurysms are asymptomatic
and therefore remain undetected (Johnston, 2002). Autopsies have revealed that many
as 25% of the population older than 55 years undetected saccular aneurysms are found
(Rubin and Farber,1999). In the general population approximately 5% is likely to harbor
these aneurysms and 15-20% of these persons have multiple lesions (Kyriacou, 1996;
Lieber et. al., 2002). Cerebral aneurysms are highly uncommon in people younger than
20 years and very common in older people, especially above 65 years old (Lieber et al.,
2002). This indicates that not every aneurysm is life threatening. However, rupture of an
intracranial aneurysm results in subarachnoid hemorrhage (SAH), with 35% mortality
during the initial hemorrhage (Rubin et al., 1999). In case of subsequent hemorrhage the
prognosis is even worse. A total 50 to 60% of the patients with SAH will die or suffer
severe morbidity (Lieber et al., 2002). Not more than one third of the patients
eventually return to their previous occupation due to severe neuropsychological
disabilities (Lieber et al., 2002).
According to (Koivisto et al., 2000) no significant difference was detected in the
outcome one year after surgical or endovascular treatment of ruptured cerebral
aneurysms. The first outcomes of the ongoing International Subarachnoid Aneurysm
Trial (ISAT), a large scale trial on ruptured aneurysms involving 42 centers in Europe
9
and America, reported that the relative risk of death or significant disability for
endovascular patients is 22.6% lower than for surgical patients. In unruptured
aneurysms coil embolization resulted in significantly less complications than surgical
clipping (Johnston, 2000).
The decision whether intervention is recommended depends on the balance
between the risk of rupture and the risk related to the intervention itself. The mechanical
properties and loading state of the arterial wall are most important in the determination
whether rupture of the aneurysm is a serious threat. Since both parameters not be
determined adequately in vivo, accurate estimation of the risk of rupture is not possible
yet. At present, the risk of rupture is mainly associated with the maximum dimension of
the lesion even though there is controversy over the 'critical size' (Kyriacou et al.,
1996).
The loading state of the arterial wall depends on the pressure load and shear
stress. In contrast to shear stress, the pressure load is similar throughout the arterial
system. The shear rate introduced by intra-aneurysm blood flow is known to affect the
endothelial cells covering the lumen. This induces adaptation, or in aneurysms,
degradation of the arterial wall. Since the shear rate can be determined from the intra-
aneurysm flow, the development of efficient methods for in vivo flow measurements is
of interest. X-ray systems have great potential in becoming an important non-invasive
method to determine the flow properties (Kyriacou et al., 1996). However, injection of
contrast agents is required in X-ray flow visualization techniques. Knowledge on the
influence of these injections is indispensable for proper interpretation of the X-ray
images, and can be acquired via computational studies. As the intra-aneurysm flow
patterns are complex, in vitro validation is needed to obtain insight in its accuracy and
limitations. Recent studies have introduced Fluid Structure Interface (FSI) simulations
using isotropic wall properties to map regions of stress concentrations developing in the
aneurismal wall as a much better alternative to the current clinical criterion Detailed
hemodynamic in cerebral aneurysms have been investigated experimentally and
computationally to understand better the mechanisms contributing to the aneurysm
progression (Kyriacau et al., 1996). However, the mechanisms causing aneurysm still
remain to be unveiled. One of the main findings regarding aneurysm hemodynamic so
10
far is the sensitivity of the blood flow to the vascular morphology. In addition using FSI
analysis from the previous study, dynamic change in vascular morphology and
hypertensive blood pressure, which is one of the risk factors in subarachnoid
hemorrhage, affects the hemodynamic. Thus, the importance of FSI in cerebral
aneurysms is still debated because the human intracranial arteries are stiffer than the
other arteries (Paal et al., 2007), and it was asserted in an earlier computational
angiographical study that the impact of vascular motion on the hemodynamic is not
crucial.
2.2 FINITE ELEMENT ANALYSIS (FEA)
Finite element analysis is a powerful computer-based tool widely used by
engineers and scientists for understanding the mechanics of physical systems. Finite
element analysis consists of a computer model of a material or design that is stressed
and analyzed for specific results. Mathematically, the finite element analysis is used for
finding approximate solutions of partial differential equations as well as of integral
equations. In order to present unlimited degrees of freedom of structures by limited
degrees of freedom, the structures are divided into many elements (Rachel et al., 2007).
These elements are connected by joint called node and make a grid named mesh.
Several modern finite element packages include specific components such as thermal,
fluid flow, electrostatic and structural working environments.
Generally, there are two types of analysis that is two-dimensional and three-
dimensional analysis. The structural of finite element analysis usually consist either
linear or nonlinear and it does generally characterize the elements. Usually finite
element models contain tens of thousands and possibly hundreds of thousands of
elements, resulting in hundreds of thousands of simultaneous equations
(Venkatasubramaniam et al., 2004). Usefulness of the finite element analysis result
depends highly on the pre-processing stage. Thus, defining an appropriate physical
model (mathematical model, geometrical simplifications, material properties, boundary
conditions and loads) and an adapted mesh in accordance with simulation goals is a
very difficult and time-consuming task. In practice, the modeling assumptions are still
mostly based on the user's experience (Bellenger et al., 2008). By using this tool, it